Abstract
A mathematical model of the flow in a round submerged turbulent jet is considered. The model includes differential transport equations for the normal components of the Reynolds stress tensor and Rodi’s algebraic approximations for shear stresses. A theoretical-group analysis of the examined model is performed, and a reduced self-similar system of ordinary differential equations is derived and solved numerically. It is shown that the calculated results agree with available experimental data.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G. N. Abramovich, Theory of Turbulent Jets (Nauka, Moscow, 1960) [in Russian].
I. Wygnanski and H. Fiedler, “Some Measurements in the Self-Preserving Jet,” J. Fluid Mech. 38, 577–612 (1969).
N. R. Panchapakesan and J. L. Lumley, “Turbulence Measurements in Axisymmetric Jets of Air and Helium. Pt 1. Air Jet,” J. Fluid Mech. 246, 197–223 (1993).
B. E. Launder, A. P. Morse, W. Rodi, and D. B. Spalding, “The Prediction of Free Shear Flows—a Comparison of Six Turbulence Models,” NASA report No. SP-311 (Washington, 1972).
W. Rodi, “The Prediction of Free Turbulent Boundary Layers by Use of Two-Equation Model of Turbulence,” Ph. D Thesis (University of London, London, 1972).
W. Rodi, Turbulence Models and their Application in Hydraulics (University of Karlsruhe, Karlsruhe, 1980).
D. C. Wilcox, Turbulence Modeling for CFD (DCW Industr. Inc., La Canada, 1994).
J. Piquet, Turbulent Flows: Models and Physics (Springer-Verlag, Berlin, Heidelberg, 1999).
S. B. Pope, “An Explanation of the Round Jet/Plane Jet Anomaly,” AIAA J. 16 (3), 279–281 (1978).
B. B. Dally, D. F. Fletcher, and A. R. Masri, “Flow and Mixing Fields of Turbulent Bluff-Body Jets and Flames,” Combust. Theory Modelling 2, 193–219 (1998).
O. V. Kaptsov, I. A. Efremov, and A. V. Schmidt, “Self-Similar Solutions of the Second-Order Model of the Far Turbulent Wake,” Prikl. Mekh. Tekh. Fiz. 49 (2), 74–78 (2008) [Appl. Mech. Tech. Phys. 49 (2), 217–221 (2008)].
I. A. Efremov, O. V. Kaptsov, and G. G. Chernykh, “Self-Similar Solutions of Two Problems of Free Turbulence,” Mat. Model. 21 (12), 137–144 (2009).
O. V. Kaptsov, A. V. Fomina, G. G. Chernykh, and A. V. Schmidt, “Self-Similar Degeneration of the Turbulent Wake behind a Body Towed in a Passively Stratified Medium,” Prikl. Mekh. Tekh. Fiz. 53 (5), 47–54 (2012) [Appl. Mech. Tech. Phys. 53 (5), 672–678 (2012)].
O. V. Kaptsov and A. V. Schmidt, “Application of the B-Determining Equations Method to One Problem of Free Turbulence,” Symmetry, Integrability Geometry 8, 073 (2012).
A. G. Demenkov, B. B. Ilyushin, and G. G. Chernykh, “Numerical Simulation of Axisymmetric Turbulent Jets,” Prikl. Mekh. Tekh. Fiz. 49 (5), 55–60 (2008) [Appl. Mech. Tech. Phys. 49 (5), 749–753 (2008)].
A. G. Demenkov, B. B. Ilyushin, and G. G. Chernykh, “Numerical Model of Round Turbulent Jets,” J. Eng. Thermophys. 18 (1), 49–56 (2009).
L. V. Ovsyannikov, Group Analysis of Differential Equations (Nauka, Moscow, 1978; Academic Press, New York, 1982).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.V. Shmidt.
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 56, No. 3, pp. 82–88, May–June, 2015.
Rights and permissions
About this article
Cite this article
Shmidt, A.V. Self-similar solution of the problem of a turbulent flow in a round submerged jet. J Appl Mech Tech Phy 56, 414–419 (2015). https://doi.org/10.1134/S0021894415030104
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021894415030104